Discrete Stochastic Autoregressive Volatility

We use Markov chain methods to develop a flexible class of discrete stochastic autoregressive volatility (DSARV) models. Our approach to formulating the models is straightforward, and readily accommodates features such as volatility asymmetry and time-varying volatility persistence. Moreover, it produces models with a low-dimensional state space, which greatly enhances computational tractability. We illustrate the proposed methodology for both individual stock and stock index returns, and show that simple first and second order DSARV models outperform generalized autoregressive conditional heteroscedasticity and Markov-switching multifractal models in forecasting volatility